Friday, July 26, 2013

1010.1294 (Gérard Ben Arous et al.)

This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor $n^{-4/3}$, has a limiting density proportional to $x^{3k-1}e^{-x^3}$. Concerning the largest gaps, normalized by $n/\sqrt{\log n}$, they converge in ${\mathrm{L}}^p$ to a constant for all $p>0$. These results are compared with the extreme gaps between zeros of the Riemann zeta function.

Followers

About CPR

A site to capture the informal process of peer review that happens daily in academia. This is intended to be a useful resource for authors, referees, and editors of journals to optimize their publications based on input from the accumulated expertise of their community.